ISSN:
1572-9265
Keywords:
ENO recovery
;
finite volume methods
;
implicit time stepping
;
compressible flow
;
Primary: 65N40, 65D15, 76M20, 76M25
;
Secondary: 76N10, 65F10
Source:
Springer Online Journal Archives 1860-2000
Topics:
Computer Science
,
Mathematics
Notes:
Abstract Following ideas of Abgrall, four different implementations of a third-order ENO scheme on general triangulations are described and examined. Two implementations utilize implicit time stepping where the resulting linear systems are solved by means of a preconditioned GMRES method. Two other schemes are constructed using an explicit Adams method in time. Quadratic polynomial recovery is used to result in a formally third-order accurate space discretisation. While one class of implementations makes use of cell averages defined on boxes and thus is close in spirit to the finite volume idea, the second class of methods considered is completely node-based. In this second case the interpretation as a true finite volume recovery is completely lost but the recovery process is much simpler and cheaper than the original one. Although one would expect a consistency error in the finite difference type implementations no such problem ever occurred in the numerical experiments.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF02143128
Permalink
